A radar pulse repetition period estimation method based on dynamic threshold and deep physical fitting

Abstract

The application discloses a radar pulse repetition interval (PRI) estimation method based on dynamic threshold and deep physical fitting. First, the dynamic threshold is calculated based on the coefficient of variation and sensitivity parameters of the time difference of arrival (DTOA) sequence to determine the validity of the subsequence. Second, according to the modulation type, the noise points are removed by the median absolute deviation for the fixed frequency, the jump points are detected and clustered for the group variable frequency, and the independent subsequences are extracted according to the dynamic threshold by using the mean shift unsupervised clustering algorithm for the uneven frequency. Then, the time offset of each pulse in the sequence relative to the first pulse is calculated, divided by the median of the sequence, and rounded to generate a virtual pulse sequence number. Finally, the physics-informed neural networks (PINNs) are introduced, the virtual sequence is iteratively fitted by gradient descent, and the slope of the fitted straight line is taken as the final PRI estimation value. The application solves the defect that the traditional method is susceptible to noise interference, and improves the PRI estimation precision and robustness in a complex electromagnetic environment.

Description

Technical Field

[0001] This invention relates to the fields of radar signal processing and electronic countermeasures, and more specifically, to a method for estimating, sorting, and extracting parameters of the pulse repetition interval (PRI) for complex modulation type radar signals. Background Technology

[0002] In modern electronic intelligence reconnaissance and radar electronic support measures systems, the interception, sorting, and parameter estimation of radiation source signals are core components in building battlefield situational awareness and threat warning. Among these, the pulse repetition period and its variation pattern are "fingerprint"-level characteristics of radar signals, directly reflecting the radar's operating mode (such as search, track, and guidance) and potential tactical intentions. High-precision estimation of the PRI of the intercepted pulse sequence is a prerequisite for subsequent radiation source identification and jamming resource allocation.

[0003] However, with the rapid development of modern radar anti-jamming and low probability of intercept (LPI) technologies, radar signal modulation types have become increasingly complex. Traditional single-fixed-repetition-frequency (SRF) radars have gradually been replaced by non-fixed-repetition-frequency (NRF) radars with complex modulation characteristics (such as variable-repetition-frequency, multi-level staggered-repetition-frequency, and sliding-repetition-frequency). Meanwhile, in actual battlefield electromagnetic environments, the pulse data (Time of Arrival (TOA) and Time Difference of Arrival (DTOA)) intercepted by reconnaissance receivers often face extremely poor signal-to-noise ratio (SNR) conditions: on the one hand, limited by receiver sensitivity, antenna scanning modulation type, and multipath fading effects, a large number of effective pulses are lost in the received signal (i.e., missing pulses); on the other hand, interference from other radiation sources in the same frequency band and environmental thermal noise in dense environments also introduce a massive number of false pulses.

[0004] Faced with the dual challenges of poor signal-to-noise ratio and complex electromagnetic interference, existing PRI estimation and signal sorting techniques, such as cumulative difference histogram, sequence difference histogram, and least squares method, have the following technical bottlenecks in practical engineering applications:

[0005] First, the fixed pulse number threshold results in extremely poor environmental adaptability.

[0006] Existing technologies typically rely on hard-coded fixed pulse count thresholds, such as requiring a continuous match of 5 or 10 pulses, to determine the validity of a candidate PRI. This "one-size-fits-all" static threshold has a fatal flaw: in low SNR environments with high spurious activity and dense false pulses, a low fixed threshold (e.g., 3 pulses) can easily mistake random, coincidental noise for a valid signal, triggering severe false alarms; conversely, in high SNR environments with less signal dispersion but some missed pulses, a high fixed threshold can easily cause genuine short-lived signals to be discarded, resulting in missed alarms. Current technologies lack an evaluation mechanism capable of sensing the degree of spurious activity within a sequence and dynamically adjusting the judgment threshold.

[0007] Second, signal clustering and feature extraction under complex modulation types are prone to degradation.

[0008] For complex signals such as staggered repetition frequencies, the pulses of multiple sub-cycles are interleaved and superimposed, resulting in a multi-peaked distribution in the DTOA sequence. Traditional methods often use a fixed tolerance window (ToleranceBin) for histogram statistics or clustering. In practice, the periodic jitter varies greatly between different radar frequency bands and different staggered levels. A fixed tolerance can easily lead to overlap of sub-signals in adjacent staggered levels or incorrect splitting of signals within the same staggered level, resulting in "clustering degradation." For group-variable repetition frequency signals, existing technologies also struggle to accurately capture transition points (dwelling switching points) in sequences containing local noise, leading to errors in subsequent feature extraction.

[0009] Third, traditional mathematical analytical solutions are extremely sensitive to phase interference and outliers.

[0010] After pulse extraction, existing techniques typically employ a one-step least squares method to perform a univariate linear fit between the pulse arrival time (TOA) and the pulse sequence number to obtain the slope of the line (i.e., the PRI estimate). However, even after pre-filtering, some multipath noise or severe phase jitter inevitably remains in the captured sequence. The traditional least squares analytical solution is extremely sensitive to outliers; even a single severely deviating noise point can cause a drastic shift in the slope of the entire fitted line, significantly reducing the accuracy of the final PRI output.

[0011] In summary, there is an urgent need in the field for a new architecture for radar pulse repetition period estimation that can adapt to complex modulation types and effectively resist high spurious noise. Summary of the Invention

[0012] To address the existing technical problems in the background art, such as poor adaptability of fixed thresholds, easy degradation in clustering of complex modulation type signals, and extreme sensitivity of traditional mathematical analytical solutions to phase interference and outliers, the present invention aims to provide a radar pulse repetition period estimation method based on dynamic thresholding and deep physical fitting. This invention aims to provide a high-precision PRI estimation solution for complex modulation type radar signals, utilizes a data-driven dynamic sensing mechanism to solve the hard threshold failure problem, and innovatively employs the gradient descent mechanism of deep neural networks to seek a globally optimal fitting solution that is resistant to disturbances.

[0013] To achieve the above objectives, the present invention provides the following technical solution:

[0014] A radar pulse repetition period estimation method, in a pre-defined signal sorting and parameter estimation process, performs fine-tuning on a given multi-source time of arrival (TOA) and time difference of arrival (DTOA) sequence. The method includes the following core steps:

[0015] S1: Dynamic threshold calculation based on scatter perception

[0016] Breaking away from the limitations of traditional methods that rely on a fixed number of pulses to determine signal validity, this paper introduces a dynamic threshold calculation method. This method first performs statistical analysis on the input DTOA sequence, calculating its mean and standard deviation. Then, it calculates the coefficient of variation, reflecting the degree of spurious activity within the sequence, and combines this with a preset sensitivity penalty parameter to calculate a dynamic threshold.

[0017] S2: Preprocessing and sorting extraction for different radar signal modulation types

[0018] The system automatically routes signals based on the modulation type of the reconnaissance equipment. For fixed repetition frequency (RPF) signals, it uses robust statistical methods to dynamically calculate outlier thresholds and accurately remove multipath noise or spurious pulses. For variable RPF signals, it automatically detects jump points in the arrival time difference sequence based on a global benchmark, divides them into multiple dwelling segments, and merges similar segments with minimal relative errors across the time domain. For complex staggered RPF signals, it calculates adaptive bandwidth parameters and introduces an unsupervised clustering algorithm. Without pre-setting the number of staggered levels, it automatically optimizes the data density peaks and accurately extracts multi-level independent staggered subsequences, thus providing clean, high signal-to-noise ratio effective data for subsequent physical fitting.

[0019] S3: Sequence mapping of virtual pulse numbers

[0020] For TOA subsequences that are determined to be valid and cleaned, their relative offset with respect to the arrival time of the first pulse is calculated. Then, this offset is divided by the median of the subsequence and rounded down to map the pulse number of the non-uniform TOA subsequence to a virtual pulse number.

[0021] S4: Disturbance-resistant Physical Information Neural Networks (PINNs)

[0022] This approach abandons the traditional one-step least squares analytical solution, which is highly susceptible to outliers. Instead, the mapped virtual pulse sequence and its corresponding real TOA sequence are normalized bidirectionally by mean and standard deviation before being input into the physical information neural network. During training, the Adam optimizer and a cosine annealing learning rate scheduler (Cosine AnnealingLR) are used to minimize the mean squared error loss through multiple iterations (e.g., 1500 epochs). After model convergence, gradient-free network weights are extracted, and inverse normalization of physical dimensions is performed to output a PRI value with extremely high perturbation resistance.

[0023] Compared with the prior art, the present invention has the following beneficial effects:

[0024] Completely solves the problem of poor environmental adaptability caused by fixed thresholds: The "dynamic threshold calculation method" proposed in this invention endows the system with the ability to "self-perceive" the intrinsic quality of data. When the signal sequence has extremely high spuriousness (large coefficient of variation), the penalty term in the formula increases sharply, and the system automatically raises the threshold, acting like a "dynamic firewall" to minimize the probability of false alarms under extremely low signal-to-noise ratios. Conversely, when the sequence quality is excellent (minimal variance), the threshold automatically drops to the lower limit (e.g., 3 pulses), greatly saving short-term lingering pulse signals in high signal-to-noise ratio environments, and achieving adaptive environmental matching that is both lenient and strict.

[0025] Overcoming the clustering degradation bottleneck in feature extraction under complex modulation types: For complex signals such as staggered and variable repetition frequencies, this invention abandons the traditional fixed tolerance window histogram method. By introducing mean-shift unsupervised clustering technology with adaptive bandwidth based on physical parameters and a robust MAD statistical algorithm, the system can accurately anchor transition points and strip interleaved signals in continuous spatiotemporal flow without pre-setting any prior knowledge about radar staggered levels or dwell lengths. This effectively prevents "sub-signal overlap" or "cluster splitting" phenomena caused by differences in radar frequency bands and jitter rates.

[0026] Possessing extremely high parameter estimation accuracy against extreme phase interference: The core innovation of this invention lies in the introduction of a physical information neural network. The analytical solution process, originally a mathematical domain and highly sensitive to outliers, is transformed into a neural network gradient descent process smoothly controlled by the learning rate and the Adam optimizer. This mechanism naturally possesses a "low-pass filtering" characteristic during iteration, effectively resisting the pulling effect of residual strong outliers on the slope. Combined with bidirectional normalization and denormalization physical restoration techniques, the final output PRI value exhibits jitter resistance far exceeding that of traditional least-squares linear fitting, providing the purest underlying parameter features for subsequent radiation source fingerprint recognition.

[0027] Providing a white-box, interactive intelligence analysis tool: This invention embeds an interactive visualization chart generator while outputting estimated parameters. It overlays and renders complex scatter plots with a deep physical fitting baseline into an HTML interactive file that supports multi-device viewing, infinite zoom, and drag-and-drop functionality. This overcomes the "black box" drawbacks of traditional algorithms' pure data output, providing backend electronic warfare intelligence analysts with a WYSIWYG (What You See Is What You Get) intuitive auxiliary judgment tool, significantly enhancing the system's engineering application value. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the overall process of a radar pulse repetition period estimation method based on dynamic threshold and deep physical fitting, provided in an embodiment of the present invention. Detailed Implementation

[0029] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0030] Reference Figure 1 The radar pulse repetition period estimation method based on dynamic threshold and deep physical fitting provided in this embodiment of the invention can be run as a core algorithm module in an electronic reconnaissance data processing server or edge computing node with CPU or GPU computing power.

[0031] S1: Dynamic threshold calculation

[0032] Existing technologies typically use a fixed number of pulses (e.g., 5 consecutive pulses) to confirm the validity of a signal sequence, which is highly susceptible to failure in harsh electromagnetic environments. This invention introduces a data-driven self-sensing mechanism, which can be further subdivided into:

[0033] S11. Perform basic statistics on the input DTOA sequence.

[0034] Calculate its mean with standard deviation To prevent mathematical division-by-zero anomalies in extremely pure signals (standard deviation close to 0) or during quiescent periods, a small constant is introduced into the denominator in the actual underlying calculation. .

[0035] S12. Calculate the coefficient of variation and generate a dynamic threshold.

[0036] Calculate the coefficient of variation of the DTOA sequence and combine it with a preset sensitivity penalty parameter. Generate dynamic threshold :

[0037]

[0038] Example Parameter Analysis: Coefficient of Variation (CV) This directly reflects the severity of spurious contamination in that signal segment. The system is set based on prior experience. Values ​​(such as in fixed or group-repeated frequency modes) =15.0, in staggered mode =20.0). When the signal is pure, CV≈0. The system automatically probes down to its physical limit of three pulses, which greatly saves ultra-short dwell time signals in high signal-to-noise ratio environments. When signal spurious signals are severe (e.g., CV=0.5), in With a penalty of 20.0, The number of pulses instantly jumps to 13. If the actual length of the candidate subsequence is less than 13, the system will directly determine it as a false alarm caused by environmental interference and discard it, thus preventing subsequent unnecessary computational power consumption from the source.

[0039] S2. Preprocessing and Sorting Extraction

[0040] Depending on the signal modulation type, the system dynamically routes to a specific branch for preprocessing. This step can be further subdivided into:

[0041] S21. Fixed Repetition Rate Path Preprocessing

[0042] The Median Absolute Deviation (MAD) algorithm from robust statistics is used to remove outliers and noise. The system first calculates the median of the sequence. , then calculate Then, outlier filtering tolerance was set. .

[0043] Principle Explanation: The constant 3 represents the extremely famous "" in the fields of statistics and engineering. The "criteria" uses a constant of 1.4826 as a scaling factor to ensure that the MAD (Modal Distortion) conforms to the standard deviation under a normal distribution. The additional 0.5 is the system time quantization error tolerance, meaning the deviation from the median is greater than... DTOA will be removed directly.

[0044] S22. Preprocessing of transformer repetition frequency path

[0045] The group repetition rate will jump between different PRIs. The system extracts the global DTOA median. And set the dynamic segmentation step size. The system iterates through the sequence, and when the absolute value of the difference between adjacent DTOAs exceeds... This triggers the "stay transition point" flag, where the sequence is cut off. Subsequently, the local PRI median of each segment is extracted. If some segments are discontinuous in time but have a very small relative error (≤0.005), the system will identify them as recurrences of the same radar operating mode, and thus stitch these TOA segments across the time axis.

[0046] S23. Preprocessing of Uneven Frequency Paths

[0047] For staggered signals with multiple levels of interleaving, the system extracts the DTOA median. And calculate the bandwidth of the adaptive kernel function. The mean-shift unsupervised clustering model is initialized using this bandwidth parameter.

[0048] Principle Explanation: Unlike K-Means, which requires a preset K value, mean shift can automatically cluster towards the region with the highest data density, like "climbing a mountain," even when the number of stochastic levels is unknown. After clustering, if the number of independent cluster centers M < 2, it indicates that clustering has failed or the radar has degenerated into a fixed repetition frequency. The system automatically triggers the fallback mechanism, reverting to the processing logic of S21. If M ≥ 2, then M-level independent stochastic subsequences have been successfully separated.

[0049] S3. Virtual serial number mapping

[0050] In traditional analytical methods, the presence of "missing pulses" (lost data points) in the sequence will lead to severe misalignment in subsequent phase alignment. This invention addresses this issue in step S3, which can be further subdivided into:

[0051] S31. Get Time Offset

[0052] Obtain the time offset of each pulse relative to the first pulse in the valid TOA subsequence. ).

[0053] S32. Calculate the virtual pulse sequence number

[0054] Median using this subsequence Calculate the virtual pulse sequence number :

[0055]

[0056] Principle Explanation: The rounding operation is fault-tolerant. It forcibly maps and aligns the absolute time, which is affected by time jitter, onto a uniform integer-level "transmission sequence number" grid. Missing integer bits represent the positions that are judged as missing pulses.

[0057] S4. Disturbance-resistant deep physics fitting and restoration

[0058] To completely overcome the drawback of traditional least squares methods being extremely sensitive to residual outlier noise, this invention innovatively introduces Physical Information Neural Networks (PINNs) for parameter estimation. This step can be further subdivided into:

[0059] S41. Bidirectional Normalization

[0060] Because TOA values ​​are usually extremely high (in the millions), If the values ​​are only tens or hundreds, direct fitting can easily lead to gradient explosion. The system calculates the mean and standard deviation of the input vector X (index) and the target vector Y (time) respectively, and performs strict Z-Score zero-mean normalization.

[0061] S42. Network Iterative Optimization

[0062] Instantiate a single-layer fully connected network nn.Linear(1,1) within the PyTorch framework. Example training parameters: Employ the Adam optimizer, setting an initial learning rate LR=0.5 to strongly escape local optima. Introduce Cosine AnnealingLR to ensure smoothness in the later stages of convergence. The maximum number of iterations (Epochs) is set to 1500. The network evaluates the difference between the predicted and actual times using mean squared error (MSELoss) and updates the weights via gradient descent. Disturbance resistance advantage: The gradient-based multi-round iterative optimization process is essentially a natural "low-pass filter." Individual severely deviating noise points cannot easily alter the global straight line slope under the momentum mechanism of the Adam optimizer, resulting in an exponentially better fitting accuracy than one-step analytical least squares.

[0063] S43. Dimensional Restoration of Physical Quantities

[0064] Extracting gradient-free weights after model convergence The inverse normalization formula is used to restore the physical quantities to their true dimensions:

[0065]

[0066] Output This is the estimated value of the pulse repetition period (PRI).

[0067] As a supporting engineering output of this invention, the system acquires... Then, the Plotly front-end visualization engine is invoked to generate an interactive HTML report. The program maps the cleaned subsequences to two-dimensional scatter points (X-axis for virtual sequence numbers, Y-axis for arrival time) and overlays the deep learning-fitted straight lines onto them. The output charts support interactive operations such as local infinite zoom and hovering over data points, providing radar signal intelligence analysts with intuitive white-box judgment criteria.

[0068] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention.

Claims

1. A radar pulse repetition period estimation method, applied to a computing device for processing radar signals with complex modulation types, characterized in that, This method, within a pre-defined signal sorting and parameter estimation process, performs fine-tuning on a given sequence of Time of Arrival (TOA) and Time Difference of Arrival (DTOA) of radiation sources. The method includes: S1: Based on the statistical characteristics of the DTOA sequence, a dynamic threshold is calculated using a statistical characteristic-based method that combines the coefficient of variation with a preset sensitivity parameter, and the validity of the signal subsequence is determined by this dynamic threshold. S2: Based on the signal modulation type of the radiation source, outlier noise removal or clustering segmentation is performed on the input TOA and DTOA sequences to extract candidate TOA sub-sequences and DTOA sub-sequences. It is then determined whether the number of pulses in each candidate sub-sequence reaches the dynamic threshold. Sub-sequences that do not reach the threshold are discarded as false alarms, thereby extracting the valid TOA and DTOA sub-sequences of the sub-signals. S3: Construct virtual pulse sequence number features for subsequences that are determined to be valid; S4: Using a physical information neural network, perform neural network fitting optimization on the virtual pulse sequence feature and the corresponding TOA subsequence to generate a high-precision pulse repetition period.

2. The method according to claim 1, characterized in that, The dynamic threshold calculation method in S1 has a dynamic threshold. The computational logic specifically includes: S11: Calculate the mean of the DTOA sequence with standard deviation ; S12: Calculate the coefficient of variation (CV) Based on preset sensitivity parameters, and The dynamic threshold for raising the value is calculated using the following formula: Among them, the Used to adjust the penalty for signal dispersion.

3. The method according to claim 1, characterized in that, The step of extracting the TOA subsequence and DTOA subsequence of the effective sub-signal in S2 includes three main branches: S21: When the signal modulation type of the radiation source is fixed repetition rate, calculate the median of the DTOA sequence, and calculate the outlier threshold based on the median absolute deviation (MAD). Use this threshold to filter out stray pulses to generate a cleaned subsequence. S22: When the signal modulation type of the radiation source is group-variable repetition frequency, a dynamic segmentation threshold is set based on the global DTOA median, the jump points of the DTOA sequence are detected and segmented; the local PRI median of each segment is extracted, and the local PRI of each segment is clustered using relative error tolerance, and the TOA segments belonging to the same PRI group are spliced ​​and fused. S23: When the signal modulation type of the radiation source is staggered frequency repetition, the dynamic bandwidth is calculated based on the median of the DTOA sequence, and the DTOA sequence is clustered using the mean-shift unsupervised clustering algorithm to identify multi-level staggered center points and extract the subsequences corresponding to each cluster.

4. The method according to claim 3, characterized in that, The underlying feature calculation and threshold segmentation steps for preprocessing each modulation type sequence in S2 specifically include: When performing step S21, the formula for calculating the median absolute deviation is as follows: And set filter tolerance These should be removed. The global median of the arrival time difference sequence is given, and the constant 3 represents the extremely well-known "... in statistics and engineering"... The "criteria" and the constant 1.4826 are scaling factors to ensure that MAD conforms to the standard deviation under a normal distribution. The preset system time quantization error tolerance; When performing S22, a dynamic segmentation threshold is set. When the absolute value of the difference between adjacent DTOA values ​​is greater than the stated value... The corresponding position is then divided into dwell segments. Here, the constant 0.05 represents a 5% relative error tolerance. The median of the global arrival time difference is used as the benchmark for the grouped repetition frequency sequence, and the constant 2.0 represents the absolute time error baseline; When performing S23, the median of DTOA is used. Calculate adaptive bandwidth parameters based on the baseline The clustering iteration is performed using this parameter. If the number of cluster centers M generated is less than 2, the clustering is considered degenerate, and the process automatically reverts to the S21 processing flow. The constant 1.5 provides an absolute lower bound that is not easily broken down for the adaptive bandwidth.

5. The method according to claim 1, characterized in that, The step of constructing the virtual pulse sequence number feature in S3 specifically includes: S31: Calculate the relative time offset of the effective TOA subsequence with respect to the arrival time of its first pulse; S32: Divide the relative time offset by the median of the subsequence and perform a rounding operation on the result to generate a discrete virtual pulse number.

6. The method according to claim 1, characterized in that, The steps in S4 for performing neural network fitting optimization and physical parameter restoration specifically include: S41: Calculate the mean and standard deviation of the virtual pulse sequence number and the TOA subsequence, and perform mean-standard deviation bidirectional normalization processing; S42: Input the normalized data into the physical information neural network, and use the Adam optimizer and cosine annealing learning rate scheduler to perform multiple rounds of iterative training to minimize the mean square error loss. S43: Extract gradient-free weights after training convergence Combining the normalized statistics in S41 with the inverse normalization of physical dimensions, the calculation formula is as follows: in, This is the estimated value of the restored pulse repetition period. The standard deviation after two-way normalization. To prevent division by zero constant.

7. The method according to any one of claims 1 to 6, characterized in that, Following S4, the method further includes an interactive visualization step: Construct an independent visual interactive page, map the TOA subsequence of the effective sub-signal to a scattered trajectory, map the estimated pulse repetition period to a physically fitted straight line, and overlay and render it into an interactive HTML file output that supports scaling and dragging.

8. A computing device comprising a processor and a memory, the memory storing a computer program which, when executed by the processor, implements the method as described in any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method as described in any one of claims 1 to 7.

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